Function integrateQAWS

Calculate an integral over the finite interval (a,b), where the integrand has algebraic and/or logarithmic endpoint singularities of a known type.

Result!Real integrateQAWS(Func, Real) (
  scope Func f,
  Real a,
  Real b,
  Real alpha,
  Real beta,
  Weight weight,
  Real epsRel = cast(Real)1e-06,
  Real epsAbs = cast(Real)0
);

The integrand is taken to be on the form 

            alpha        beta
f(x) (x - a)      (b - x)     w(x)

where f(x) is the given function and w(x) is specified by setting the weight parameter to one of the following: 

Weight.unity:  w(x) = 1
Weight.logxa:  w(x) = log(x-a)
Weight.logbx:  w(x) = log(b-x)
Weight.logab:  w(x) = log(x-a) log(b-x)

A globally adaptive subdivision strategy is applied, with modified Clenshaw–Curtis integration on those subintervals which contain a or b.

Example

// Calculate the integral of 1/(sqrt(1-x^^2) * (x+1.5)).
// Another way to write this integrand is
//     (x-(-1))^^(-0.5) * (1-x)^^0.5 / (x+1.5),
// so we set alpha = beta = -0.5.
real f(real x) { return 1/(x + 1.5L); }
auto i = integrateQAWS(&f, -1.0L, 1.0L, -0.5L, -0.5L, Weight.unity, 1e-15L);